A mode-independent H∞ filter design for discrete-time Markovian jump linear systems

This paper addresses the problem of H_∞ filtering for discrete-time linear systems with Markovian jumping parameters. The main contribution of the paper is to provide a linear matrix inequality approach for designing an asymptotically stable linear time-invariant H_∞ filter for systems where the jumping parameter is not accessible. The cases where the transition probability matrix of the Markov chain is either exactly known, or unknown but belongs to a given polytope, are treated. The robust H_∞ filtering problem where the system matrices for each operating mode are unknown but belongs to a given polytope is also considered. A new internal mean square stability condition as well as a bounded real lemma for discrete-time Markovian jump linear systems are also developed.